Design of Perimeter Estimators for Digitized Planar Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
A New Parameterization of Digital Straight Lines
IEEE Transactions on Pattern Analysis and Machine Intelligence
A new characterization of digital lines by least square fits
Pattern Recognition Letters
On the recognition of digital circles in linear time
Computational Geometry: Theory and Applications
A parametrization of digital planes by least-squares fits and generalizations
Graphical Models and Image Processing
Digitized Circular Arcs: Characterization and Parameter Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ellipses Estimation from their Digitization
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
The Reconstruction of the Digital Hyperbola Segment from Its Code
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
On Characterization of Discrete Triangles by Discrete Moments
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Digital and image geometry
On discrete triangles characterization
Computer Vision and Image Understanding
On the Number of Digital Discs
Journal of Mathematical Imaging and Vision
The Number of N-Point Digital Discs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Representation and reconstruction of fuzzy disks by moments
Fuzzy Sets and Systems
Ellipse detection with elemental subsets
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Ellipse detection through decomposition of circular arcs and line segments
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
On the number of digitizations of a disc depending on its position
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Estimation of moments of digitized objects with fuzzy borders
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
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In this paper, our studies are focused on ellipses and problems related to their representation and reconstruction from the data resulting from their digitization. The main result of the paper is that a finite number of discrete moments, corresponded to digital ellipses, is in one-to-one correspondence with digital ellipses, which enables coding of digital ellipses with an asymptotically optimal amount of memory. In addition, the problem of reconstruction, based on the same parameters, is considered. Since the digitization of real shapes causes an inherent loss of information about the original objects, the precision of the original shape estimation from the corresponding digital data is limited. We derive a sharp upper bound for the errors in reconstruction of the center position and half-axes of the ellipse, in function of the applied picture resolution (i.e., the number of pixels per unit). An extension of these results to the $3D$ case is also given.